What is the Optimal Size of the Quantum Region in Embedding Calculations of Two-Photon Absorption Spectra of Fluorescent Proteins?

We
systematically investigate an impact of the size and content
of a quantum (QM) region, treated at the density functional theory
level, in embedding calculations on one- (OPA) and two-photon absorption
(TPA) spectra of the following fluorescent proteins (FPs) models: Aequorea victoria green FP (avGFP) with neutral (avGFP-n)
and anionic (avGFP-a) chromophore as well as Citrine FP. We find that
amino acid (a.a.) residues as well as water molecules hydrogen-bonded
(h-bonded) to the chromophore usually boost both OPA and TPA processes
intensity. The presence of hydrophobic a.a. residues in the quantum
region also non-negligibly affects both absorption spectra but decreases
absorption intensity. We conclude that to reach a quantitative description
of OPA and TPA spectra in multiscale modeling of FPs, the quantum
region should consist of a chromophore and most of a.a. residues and
water molecules in a radius
of 0.30–0.35 nm (ca. 200–230 atoms)
when the remaining part of the system is approximated by the electrostatic
point-charges. The optimal size of the QM region can be reduced to
80–100 atoms by utilizing a more advanced polarizable embedding
model. We also find components of the QM region that are specific
to a FP under study. We propose that the F165 a.a. residue is important
in tuning the TPA spectrum of avGFP-n but not other investigated FPs.
In the case of Citrine, Y203 and M69 a.a. residues must definitely
be part of the QM subsystem. Furthermore, we find that long-range
electrostatic interactions between the QM region and the rest of the
protein cannot be neglected even for the most extensive QM regions
(ca. 350 atoms).